Reciprocal Prime Magic Squares - Joel Haddley
24th November 2012
It is well known that rational numbers are numbers whose decimal expansions either terminate or repeat indefinitely. If \(p\) is a prime number, it turns out that the numbers in its decimal expansion repeat with period dividing \(p-1\). We will explain why this happens, state under what condition the period is exactly \(p-1\), and explain how all of this relates to magic squares such as:
1 |
4 |
2 |
8 |
5 |
7 |
2 |
8 |
5 |
7 |
1 |
4 |
4 |
2 |
8 |
5 |
7 |
1 |
5 |
7 |
1 |
4 |
2 |
8 |
7 |
1 |
4 |
2 |
8 |
5 |
8 |
5 |
7 |
1 |
4 |
2 |